A firm uses three types of factor input, namely labour, capital and raw material in producing two products, X and Y. Each unit of X contributes 2 Ghana cedis to profit whereas each unit of Y contributes 3 Ghana cedis to profit. To produce one unit of X requires one unit of labour, one unit of capital and two units of raw material. To produce one unit of Y requires one unit of labour, two units of capital, and one unit of raw material. The firm has 50 units of labour, 80 units of capital, and 80 units raw material available. Required: (a) Formulate the linear programming model (b) Find the feasible output combination of products X and Y which will maximize profit for the producer. (c) What is the value of total profit at this combination?.
A firm uses three types of factor input, namely labour, capital and raw material in producing two products, X and Y. Each unit of X contributes 2 Ghana cedis to profit whereas each unit of Y contributes 3 Ghana cedis to profit. To produce one unit of X requires one unit of labour, one unit of capital and two units of raw material. To produce one unit of Y requires one unit of labour, two units of capital, and one unit of raw material. The firm has 50 units of labour, 80 units of capital, and 80 units raw material available. Required: (a) Formulate the linear programming model (b) Find the feasible output combination of products X and Y which will maximize profit for the producer. (c) What is the value of total profit at this combination?.
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